We compare the performance of our proposed scheme with the two-level ADMM algorithm proposed in [1]}.
Since the latter uses Gauss-Seidel or sequential updating rules, which are not amenable to distributed parallelization, the two algorithms are not directly comparable.
Therefore, to solve the multi-period ACOPF with the two-level algorithm, we reformulate it using the variable splitting technique described in [1]}.
Specifically, for each \(t \in [T]\) , we introduce a so-called global copy \(\bar{p}^g_t\)  of \(p^g_t\) ,
and for each \(t \in [T-1]\) , we introduce a so-called local copy \(\hat{p}^{g}_{t+1}\)  (local to block \(t+1\) ) of \(p^g_{t}\) .
The ramping limit for period \(t \in [T-1]\)  is then expressed as:
\(p^g_{i,t+1} - \hat{p}^g_{i,t+1} + s^g_{i,t+1} = r_{i} \Delta _t\) ,
which is added as an additional constraint to \(X_{t+1}\) .
Finally, the coupling constraints linking the various blocks can be expressed as:
\(p^g_{t} = \bar{p}^g_t\)  for \(t \in [T]\) ,
and
\(\hat{p}^g_{t+1} = \bar{p}^g_t\)  for \(t \in [T-1]\) .
For brevity, we consider only the 118-bus case with a ramp limit of \(0.33\%\) .
